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Research Article | Open Access

Pointwise potential estimates for solutions to a class of nonlinear elliptic equations with measure data

Zhaoyue Sui, Feng Zhou( )
School of Mathematics and Statistics, Shandong Normal University, Jinan, Shandong, 250358, China
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Abstract

In this article, we investigate the regularities of solutions to a class of nonlinear elliptic equations with measure data. These equations involve the N-functions, and the solutions belong to the Sobolev-Orlicz spaces. Through the application of comparison arguments, Caccioppoli-type inequality, and maximal estimate, we derive pointwise Riesz potential estimates for both the gradient of the solutions and the solutions themselves. Furthermore, we establish Hölder continuity estimates for the solutions.

Keywords

Riesz potentialnonlinear elliptic equationsregularitySobolev-Orlicz spaces
CLC number: 35J60, 35R05, 35R06

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AIMS Mathematics
Volume 10 Issue 4,
April 2025
Pages 8066-8094
DOI: 10.3934/math.2025370

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Cite this article:
Sui Z, Zhou F. Pointwise potential estimates for solutions to a class of nonlinear elliptic equations with measure data. AIMS Mathematics, 2025, 10(4): 8066-8094. https://doi.org/10.3934/math.2025370

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Received: 17 January 2025
Revised: 19 March 2025
Accepted: 24 March 2025
Published: 15 April 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)